Constant term - fixed effects

[Magnus Justad]

Dear all,

This might be a silly question, however, can't find any information about it online (there is a lot on the constant term but little when dealing with its significance). I understand that the constant of the fixed effects regression (-xtreg, fe-) is the average value of the fixed effects across the entities. I have a non-significant constant coefficient - i.e. the average fixed effects are not significantly different from zero. Does this imply that the fixed effects model is not to be preferred? Or is it simply that the fixed effects, on average, is low such that it is insignificant thus a fixed effects model would still be appropriate?

Thank you in advance!

Best,
Magnus

[Carlo Lazzaro]

Magnus:
what does the F test at the foot of the outcome table tell?

[Magnus Justad]

Carlo Lazzaro The F-test is 0.0001. So in terms of the F-test all the coefficients are not different from zero. Thoughts?

[Carlo Lazzaro]

Magnus:
I would go -xtreg, fe- regardless the constant.
I assume that you have already performed a -hausman- test to choose between -fe- and -re- specification and contrasted the results of -hausman- test against the literature of your research field.

[Magnus Justad]

Dear Carlo, thank you for your assistance. Indeed, the Hausman test indicates fixed effects, in addition to previous literature.

Thank you for helpful comments!

Best,
Magnus

[mohina saxena]

Hello All,

I am facing a similar problem; while performing fixed effects model, I find the intercept to be negative and insignificant. How do I interpret such a negative average fixed effects value?
Does this simply mean that the expected value of my dependent variable would be less than zero (as the average of fixed effects computed from fixed effects of all the groups is negative) when all explanatory variables are zero? Is it correct interpretation?

I understand an average can be negative but average of fixed effects being negative is vague to me. I am not able to visualize it. I am thinking of it as the fixed effect of some group is negative which is making the whole average (and therefore the constant term in regression) to be negative, am I right here?

Can someone help in clarifying this doubt please?

Also, the Hausman test indicates the use of fixed effects only.

[Jordan Sydenham]

Mohina:

I believe that the interpretation you have provided above is correct, i.e. this simply means that the expected value of my dependent variable would be less than zero (as the average of fixed effects computed from fixed effects of all the groups is negative) when all explanatory variables are zero. As Carlo pointed out in the prior comments what is of more importance in the overall significance of the model (the F-test). I do not know the exact nature of your study, however in most studies the constant term is of little importance and what really matters are the results as regards to what you are investigating. In essence a negative and non-significant value for an intercept term in a fixed effect model is not really an issue.

Kind regards,
Jordan

[mohina saxena]

Many Thanks Jordan for the clarification.

regards
Mohina

[mohina saxena]

Hello All,

In another of my estimation I find the constant term after performing Fixed effects turns out to be significant at 1%. In fact the coefficient value is higher in magnitude than most of the explanatory variables. I do understand the usual interpretation of intercept term using FE but what I am curious to know does this in any sense imply that I have an omitted variable bias in the model? Need some thoughts on this. Please help in resolving.

P.S. Hausman test indicated use of FE.

Stay safe and regards,
Mohina

[Carlo Lazzaro]

Mohina:
as per FAQ, please provide wht you typed and what Stata gave you back.
That said, I'm not aware of the significance of (basically immaterial) _cons in -xtreg,fe- as an acid test for model misspecification.
In order to check that, you have to draw upon the methodology reported under -linktest- entry, Stata .pdf manual:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage c.age##c.age i.year, fe

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1162                                         min =          1
     between = 0.1078                                         avg =        6.1
     overall = 0.0932                                         max =         15

                                                F(16,23784)       =     195.45
corr(u_i, Xb)  = 0.0613                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0728746   .0107894     6.75   0.000     .0517267    .0940224
             |
 c.age#c.age |  -.0010113    .000061   -16.57   0.000    -.0011309   -.0008917
             |
        year |
         69  |   .0647054   .0158222     4.09   0.000     .0336928     .095718
         70  |   .0284423   .0234621     1.21   0.225     -.017545    .0744295
         71  |   .0579959   .0326524     1.78   0.076    -.0060048    .1219967
         72  |   .0510671   .0422995     1.21   0.227    -.0318426    .1339769
         73  |   .0424104    .052118     0.81   0.416    -.0597442    .1445651
         75  |   .0151376   .0717194     0.21   0.833    -.1254371    .1557123
         77  |   .0340933   .0918106     0.37   0.710    -.1458613    .2140478
         78  |   .0537334   .1023339     0.53   0.600    -.1468475    .2543143
         80  |   .0369475   .1221806     0.30   0.762    -.2025343    .2764293
         82  |   .0391687   .1423573     0.28   0.783    -.2398606     .318198
         83  |    .058766   .1523743     0.39   0.700    -.2398974    .3574294
         85  |   .1042758   .1726431     0.60   0.546    -.2341157    .4426673
         87  |   .1242272   .1930108     0.64   0.520    -.2540863    .5025406
         88  |   .1904977   .2068016     0.92   0.357    -.2148466     .595842
             |
       _cons |   .3937532   .2001741     1.97   0.049     .0013992    .7861072
-------------+----------------------------------------------------------------
     sigma_u |  .40275174
     sigma_e |  .30127563
         rho |  .64120306   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23784) = 8.75                 Prob > F = 0.0000

. predict fitted, xb
(24 missing values generated)

. g sq_fitted=fitted^2
(24 missing values generated)

. xtreg ln_wage c.age##c.age i.year fitted sq_fitted , fe
note: c.age#c.age omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1173                                         min =          1
     between = 0.1121                                         avg =        6.1
     overall = 0.0952                                         max =         15

                                                F(17,23783)       =     185.82
corr(u_i, Xb)  = 0.0636                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |  -.0004375   .0101809    -0.04   0.966    -.0203927    .0195177
             |
 c.age#c.age |          0  (omitted)
             |
        year |
         69  |   -.016534   .0167255    -0.99   0.323    -.0493171    .0162491
         70  |  -.0127288   .0237179    -0.54   0.591    -.0592175    .0337599
         71  |  -.0164466   .0331484    -0.50   0.620    -.0814196    .0485264
         72  |    -.01567   .0426408    -0.37   0.713    -.0992486    .0679087
         73  |  -.0163476   .0523761    -0.31   0.755     -.119008    .0863128
         75  |  -.0170026   .0718037    -0.24   0.813    -.1577425    .1237373
         77  |  -.0111413   .0919053    -0.12   0.904    -.1912815    .1689988
         78  |  -.0029997   .1024755    -0.03   0.977    -.2038583    .1978589
         80  |  -.0007318   .1222162    -0.01   0.995    -.2402832    .2388196
         82  |   .0058067   .1423696     0.04   0.967    -.2732467    .2848601
         83  |   .0158354    .152445     0.10   0.917    -.2829665    .3146373
         85  |     .04142   .1729275     0.24   0.811    -.2975289     .380369
         87  |   .0523993   .1933303     0.27   0.786    -.3265405     .431339
         88  |   .0938441   .2077193     0.45   0.651     -.313299    .5009872
             |
      fitted |   5.201776   .7930936     6.56   0.000     3.647262     6.75629
   sq_fitted |  -1.321262   .2486689    -5.31   0.000    -1.808669    -.833855
       _cons |  -3.307108   .6559794    -5.04   0.000    -4.592869   -2.021346
-------------+----------------------------------------------------------------
     sigma_u |  .40189262
     sigma_e |   .3011033
         rho |  .64048345   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23783) = 8.73                 Prob > F = 0.0000

. test sq_fitted

 ( 1)  sq_fitted = 0

       F(  1, 23783) =   28.23
            Prob > F =    0.0000

.

The -test- outcome on -sq_fitted- performed as a postestimation test on the augmented regression, tells that the model is misspecified.

[mohina saxena]

Dear Carlo,

Many Thanks for the help. I read more about it and could work it out.

regards,
Mohina